UEL

$F^N=F^N\left(u^M,H^{\alpha },p^{\beta },t\right)$, where the residual force is the external force minus the internal force.

Automatic convergence checks are applied to the force residuals corresponding to degrees of freedom 1–7.

You must define AMATRX$=K^{NM}=-\partial F^N/\partial u^M$ and RHS$=F^N$ and update the state variables, $H^{\alpha }$.

$F^N=F^N\left(u^M,H^{\alpha },p^{\beta }\right)$, where $p^{\beta }=p_0^{\beta }+\lambda q^{\beta }$, $p_0^{\beta }$ and $q^{\beta }$ are fixed load parameters, and $\lambda$ is the Riks (scalar) load parameter.

Automatic convergence checks are applied to the force residuals corresponding to degrees of freedom 1–7.

You must define AMATRX$=K^{NM}=-\partial F^N/\partial u^M$, RHS(1)$=F^N$, and RHS(2)$=\mathrm{\Delta }\lambda \left(\partial F^N/\partial \lambda \right)$ and update the state variables, $H^{\alpha }$. RHS(2) is the incremental load vector.

Automatic convergence checks are applied to the force residuals corresponding to degrees of freedom 1–7.

LFLAGS(3)=1: Normal time increment. Either the Hilber-Hughes-Taylor or the backward Euler time integration scheme will be used. With $\alpha$ set to zero for the backward Euler, both schemes imply

where $M^{NM}=M^{NM}\left(u^M,{\dot{u}}^M,H^{\alpha },p^{\beta },t,\mathrm{\dots }\right)$ and $G^N=G^N\left(u^M,{\dot{u}}^M,H^{\alpha },p^{\beta },t,\mathrm{\dots }\right)$; that is, the highest time derivative of $u^M$ in $M^{NM}$ and $G^N$ is ${\dot{u}}^M$, so that

Therefore, you must store $G_t^N$ as an internal state vector. If half-increment residual calculations are required, you must also store $G_{t^{-}}^N$ as an internal state vector, where $t^{-}$ indicates the time at the beginning of the previous increment. For $\alpha =0$, $F^N=-M^{NM}\ddot{u}{}_{t+\mathrm{\Delta }t}+G^N{}_{t+\mathrm{\Delta }t}$ and $G_t^N$ is not needed. You must define AMATRX$=M^{NM}\left(d\ddot{u}/du\right)+\left(1+\alpha \right)C^{NM}\left(d\dot{u}/du\right)+\left(1+\alpha \right)K^{NM},$ where $C^{NM}=-\partial G^N{}_{t+\mathrm{\Delta }t}/\partial {\dot{u}}^M$ and $K^{NM}=-\partial G^N{}_{t+\mathrm{\Delta }t}/\partial u^M$. RHS$=F^N$ must also be defined and the state variables, $H^{\alpha }$, updated. Although the value of $\alpha$ given in the dynamic step definition is passed into UEL, the value of $\alpha$ can vary from element to element. For example, $\alpha$ can be set to zero for some elements in the model where numerical dissipation is not desired.

LFLAGS(3)=5: Half-increment residual ($F_{1/2}^N$) calculation. Abaqus/Standard will adjust the time increment so that $max\left|F_{1/2}^N\right|<tolerance$ (where $tolerance$ is specified in the dynamic step definition). The half-increment residual is defined as

where $t^{-}$ indicates the time at the beginning of the previous increment ($\alpha$ is a parameter of the Hilber-Hughes-Taylor time integration operator and will be set to zero if the backward Euler time integration operator is used). You must define RHS$=F_{1/2}^N$. To evaluate $M^{NM}$ and $G^N{}_{t+\mathrm{\Delta }t/2}$, you must calculate $H^{\alpha }{}_{t+\mathrm{\Delta }t/2}$. These half-increment values will not be saved. DTIME will still contain $\mathrm{\Delta }t$ (not $\mathrm{\Delta }t/2$). The values contained in U, V, A, and DU are half-increment values.

LFLAGS(3)=4: Velocity jump calculation. Abaqus/Standard solves $-M^{NM}\mathrm{\Delta }{\dot{u}}^M=0$ for $\mathrm{\Delta }{\dot{u}}^M$, so you must define AMATRX$=M^{NM}$.

LFLAGS(3)=6: Initial acceleration calculation. Abaqus/Standard solves $-M^{NM}{\ddot{u}}^M+G^N=0$ for ${\ddot{u}}^M$, so you must define AMATRX$=M^{NM}$ and RHS$=G^N$.

The requirements are identical to those of static analysis, except that the Jacobian (stiffness), AMATRX, is not required. No convergence checks are performed in this case.

The requirements are identical to those of static analysis.

The requirements are identical to those of static analysis, except that the automatic convergence checks are applied to the heat flux residuals corresponding to degrees of freedom 11, 12, …

Automatic convergence checks are applied to the heat flux residuals corresponding to degrees of freedom 11, 12, …

The backward difference scheme is always used for time integration; that is, Abaqus/Standard assumes that ${\dot{u}}_{t+\mathrm{\Delta }t}=\mathrm{\Delta }u/\mathrm{\Delta }t$, where $\mathrm{\Delta }u=u_{t+\mathrm{\Delta }t}-u_t$ and so $d\dot{u}/du=1/\mathrm{\Delta }t$ always. For degrees of freedom 11, 12, …, $max\left|\mathrm{\Delta }u\right|$ will be compared against the user-prescribed maximum allowable nodal temperature change in an increment, $\mathrm{\Delta }{\theta }_{max}$, for controlling the time integration accuracy.

You need to define AMATRX$=K^{NM}+\left(1/\mathrm{\Delta }t\right)C^{NM}$, where $C^{NM}$ is the heat capacity matrix and RHS$=F^N$, and must update the state variables, $H^{\alpha }$.

Identical to static analysis, except that the automatic convergence checks are applied to the residuals corresponding to degrees of freedom 1–8.

Identical to static analysis, except that the automatic convergence checks are applied to the residuals corresponding to degrees of freedom 1–8.

Automatic convergence checks are applied to the residuals corresponding to degrees of freedom 1–8.

The backward difference scheme is used for time integration; that is, ${\dot{u}}_{t+\mathrm{\Delta }t}^M=\mathrm{\Delta }{u}^M/\mathrm{\Delta }t$, where $\mathrm{\Delta }{u}^M=u_{t+\mathrm{\Delta }t}^M-u_t^M$.

For degree of freedom 8, $max\left|\mathrm{\Delta }{u}^M\right|$ will be compared against the user-prescribed maximum wetting liquid pore pressure change, $\mathrm{\Delta }{u}_w^{max}$, for automatic control of the time integration accuracy.

You must define AMATRX$=K^{NM}+\left(1/\mathrm{\Delta }t\right)C^{NM}$, where $C^{NM}$ is the pore fluid capacity matrix and RHS$=F^N$, and must update the state variables, $H^{\alpha }$.

Identical to static analysis, except that the automatic convergence checks are applied to the residuals corresponding to degrees of freedom 1–7 and 11, 12, …

Automatic convergence checks are applied to the residuals corresponding to degrees of freedom 1–7 and 11, 12, …

The backward difference scheme is used for time integration; that is, ${\dot{u}}_{t+\mathrm{\Delta }t}^M=\mathrm{\Delta }{u}^M/\mathrm{\Delta }t$, where $\mathrm{\Delta }{u}^M=u_{t+\mathrm{\Delta }t}^M-u_t^M$.

For degrees of freedom 11, 12, …, $max\left|\mathrm{\Delta }{u}^M\right|$ will be compared against the user-prescribed maximum allowable nodal temperature change in an increment, $\mathrm{\Delta }{\theta }_{max}$, for automatic control of the time integration accuracy.

You must define AMATRX$=K^{NM}+\left(1/\mathrm{\Delta }t\right)C^{NM}$, where $C^{NM}$ is the heat capacity matrix and RHS$=F^N$, and must update the state variables, $H^{\alpha }$.

The requirements are identical to those of static analysis, except that the automatic convergence checks are applied to the current density residuals corresponding to degree of freedom 9, in addition to the heat flux residuals.

Automatic convergence checks are applied to the current density residuals corresponding to degree of freedom 9 and to the heat flux residuals corresponding to degree of freedom 11.

The backward difference scheme is always used for time integration; that is, Abaqus/Standard assumes that ${\dot{u}}_{t+\mathrm{\Delta }t}=\mathrm{\Delta }u/\mathrm{\Delta }t$, where $\mathrm{\Delta }u=u_{t+\mathrm{\Delta }t}-u_t$. Therefore, $d\dot{u}/du=1/\mathrm{\Delta }t$ always. For degree of freedom 11 $max\left|\mathrm{\Delta }u\right|$ will be compared against the user-prescribed maximum allowable nodal temperature change in an increment, $\mathrm{\Delta }{\theta }_{max}$, for controlling the time integration accuracy.

You must define AMATRX$=K^{NM}+\left(1/\mathrm{\Delta }t\right)C^{NM}$, where $C^{NM}$ is the heat capacity matrix and RHS$=F^N$, and must update the state variables, $H^{\alpha }$.

Identical to static analysis, except that the automatic convergence checks are applied to the residuals corresponding to degrees of freedom 1–7, 9, and 11.

Automatic convergence checks are applied to the residuals corresponding to degrees of freedom 1–7, 9, and 11.

The backward difference scheme is always used for time integration; that is, Abaqus/Standard assumes that ${\dot{u}}_{t+\mathrm{\Delta }t}=\mathrm{\Delta }u/\mathrm{\Delta }t$, where $\mathrm{\Delta }u=u_{t+\mathrm{\Delta }t}-u_t$. Therefore, $d\dot{u}/du=1/\mathrm{\Delta }t$ always. For degree of freedom 11 $max\left|\mathrm{\Delta }u\right|$ will be compared against the user-prescribed maximum allowable nodal temperature change in an increment, $\mathrm{\Delta }{\theta }_{max}$, for controlling the time integration accuracy.

You must define AMATRX$=K^{NM}+\left(1/\mathrm{\Delta }t\right)C^{NM}$, where $C^{NM}$ is the heat capacity matrix and RHS$=F^N$; and you must update the state variables, $H^{\alpha }$.

Abaqus/Standard will solve $K^{NM}{\tilde{u}}^M={\tilde{P}}^N$ for ${\tilde{u}}^M$, where $K^{NM}$ is the base state stiffness matrix and the perturbation load vector, ${\tilde{P}}^N$, is a linear function of the perturbation loads, $\tilde{p}$; that is, ${\tilde{P}}^N=\left(\partial F/\partial \tilde{p}\right)\tilde{p}$.

LFLAGS(3)=1: You must define AMATRX$=K^{NM}$ and RHS$={\tilde{P}}^N$.

LFLAGS(3)=100: You must compute perturbations of the internal variables, ${\tilde{H}}^{\alpha }$, and define RHS$={\tilde{P}}^N-K^{NM}{\tilde{u}}^M$ for output purposes.

$F^N=-M^{NM}\ddot{\tilde{u}}+G^N\left(u^M+{\tilde{u}}^M,\mathrm{\dots }\right)=-M^{NM}\ddot{\tilde{u}}+\left(\partial G^N/\partial u^M\right){\tilde{u}}^M$.

Abaqus/Standard will solve $K^{NM}{\varphi }_i^M\mathit{ }={\omega }_i^2{M}^{NM}{\varphi }_i^M$ for ${\varphi }_i^N$ and ${\omega }_i$, where $K^{NM}=-\partial F^N/\partial u^M$ is the base state stiffness matrix and $M^{NM}=-\partial F^{NM}/\partial {\ddot{u}}^M$ is the base state mass matrix.

LFLAGS(3)=2: Define AMATRX$=K^{NM}$.

LFLAGS(3)=4: Define AMATRX$=M^{NM}$.

LFLAGS(3)=2: Define stiffness matrix AMATRX $=K^{NM}$ .

LFLAGS(3)=4: Define mass matrix AMATRX $=M^{NM}$ .

LFLAGS(3)=3: Define damping matrix AMATR $=C^{NM}$ .

LFLAGS(3)=2: Define stiffness matrix AMATRX $=K^{NM}$ .

LFLAGS(3)=4: Define mass matrix AMATRX $=M^{NM}$ .

LFLAGS(3)=3: Define damping matrix AMATR $=C^{NM}$ .